Question

In: Math

1-Prove the identity. cosh(x) + sinh(x) = ex cosh(x) + sinh(x) = 1 2 ex +...

1-Prove the identity.

cosh(x) + sinh(x) = e^x

cosh(x) + sinh(x)

=

1

2

e^x + e^−x

+

1

2

=

1

2

=

2-Prove the identity.

sinh(x + y) = sinh(x) cosh(y) + cosh(x) sinh(y)

sinh(x) cosh(y) + cosh(x) sinh(y)

=

1

2

(e^x − e^−x)

1

2

+

1

2

(e^x + e^−x)

1

2

=

1

4

+ e^{x − y} − e^{−x + y} − e^{−x −
y}

+

e^{x + y} − e^{x − y} + e^{−x + y} − e^{−x − y}

=

1

4

− 2e^{−x − y}

=

1

2

e^{x + y} − e^{−(x + y)}

=

3-Prove the identity.

sinh(2x) = 2 sinh(x) cosh(x)

sinh(2x)

=

sinh

x +

=

sinh(x) + cosh(x) sinh(x)

=

4-Prove the identity.

1 + tanh(x)

1 − tanh(x)

= e^2x

1 + tanh(x)

1 − tanh(x)

=

1 +

cosh(x)

1 −

cosh(x)

=

cosh(x) +

cosh(x) −

=

1

2

e^x + e^−x

+

1

2

(e^x − e^−x

1

2

e^x + e^−x

−

1

2

(e^x − e^−x

=

e^−x

=

5-If

tanh(x) =

4

5

,

find the values of the other hyperbolic functions at x.

sinh(x)	=
cosh(x)	=
coth(x)	=
sech(x)	=
csch(x)	=

Expert Solution

milcah answered 2 years ago

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Question

1-Prove the identity. cosh(x) + sinh(x) = ex cosh(x) + sinh(x) = 1 2 ex +...

Solutions

Expert Solution

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